Can we simply add stratified comprehension $SF$ to axioms of Ackermann's set theory $Ack$?
Is there a clear argument of inconsistency involved with such addition? supposing that $NF$ and $Ack$ are consistent of course.
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asked Aug 24, 2020 at 7:14
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$\begingroup$ It is not even known that $NF$ is consistent, right? $\endgroup$– MasterCommented Dec 14, 2020 at 20:13
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$\begingroup$ Yes but the argument is relative, if we suppose NF and Ack to be consistent, then is their blend consistent. By the way this question supposedly do have a positive answer according to Holmes, although he didn't write up the full formal proof, but the sketch of the proof is there and it seems convincing. $\endgroup$– Zuhair Al-JoharCommented Dec 15, 2020 at 15:29
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$\begingroup$ So you want to, from a model of $Ack$ and a model of $NF$, construct a model of $NF+Ack$? $\endgroup$– MasterCommented Dec 15, 2020 at 17:34
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$\begingroup$ Yes, something like that! $\endgroup$– Zuhair Al-JoharCommented Dec 16, 2020 at 18:26
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